Finite Group DatabasebetaFinite Group Databasebeta| order | 30624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 860160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C3×C42×C11×C29 |
| multiplicative | (ℤ/40135)ˣ, (ℤ/44695)ˣ, (ℤ/49803)ˣ, (ℤ/57465)ˣ, (ℤ/66404)ˣ, (ℤ/80270)ˣ, (ℤ/89390)ˣ, (ℤ/99606)ˣ, (ℤ/114930)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C23×C3×C11×C29 |
| socle, prime radical | C23×C3×C11×C29 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
432 conjugacy classes of subgroups.
30624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.